In this chapter, we provide NCERT Exemplar Problems Solutions for Class 7 Maths Chapter 8 Rational Numbers for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Exemplar Problems Solutions for Class 7 Maths Chapter 8 Rational Numbers pdf. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 7 |

Subject | Maths |

Chapter | Chapter 8 |

Chapter Name | Rational Numbers |

Category | NCERT Exemplar |

## NCERT Exemplar Class 7 Maths Chapter 8 Rational Numbers

**Multiple Choice Questions (MCQs)**

**Question 1:**A rational number is defined as a number that can be expressed in the form p/q, where p and q are integers and

(a) q = 0 (b) q = 1

(c) q ≠ 1 (d) q ≠ 0

**Solution :**

(d) By definition, a number that can be expressed in the form of p/q, where p and q are integers and q≠0, is called a rational number.

**Question 2:**Which of the following rational numbers is positive?

**Solution :**

(c) We know that, when numerator and denominator of a rational number, both are negative,

it is a positive rational number.

Hence, among the given rational numbers is positive.

**Question 3:**Which of the following rational numbers is negative?

**Solution :**

**Question 4:**In the standard form of a rational number, the common factor of numerator and denominator is always

(a) 0 (b) 1 c) -2 (d)2

**Solution :**

(b) By definition, in the standard form of a rational number, the common factor of numerator and denominator is always1

**Note:**Common factor means, a number which divides both the given two numbers.

**Question 5:**Which of the following rational numbers is equal to its reciprocal?

(a) 1 (b) 2 c) 1/2 (d)0

**Solution :**

**Question 6:**The reciprocal of 1/2 is

(a) 3 (b) 2 c) -1 (d)0

**Solution :**

(b) Reciprocal of =2

**Question 7:**The standard form of is

**Solution :**

**Question 8:**Which of the following is equivalent to 4/5 ?

**Solution :**

**Note:** If the numerator and denominator of a rational number is multiplied/divided by a non-zero integer, then the result we get, is equivalent rational number.

**Question 9:**How many rational numbers are there between two rational numbers?

(a) 1 (b) 0

(c) unlimited (d) 100

**Solution :**

(c) There are unlimited numbers between two rational numbers.

**Question 10:**In the standard form of a rational number, the denominator is always a

(a) 0 (b) negative integer

(c) positive integer (d) 1

**Solution :**

(c) By definition, a rational number is said to be in the standard form, if its denominator is a positive integer.

**Question 11:**To reduce a rational number to its standard form, we divide its numerator and denominator by their

(a) LCM (b) HCF

(c) product (d) multiple

**Solution :**

(b) To reduce a rational number to its standard form, we divide its numerator and denominator by their HCF.

**Question 12:**Which is greater number in the following?

(a) – (b) 0 (c) (d)-2

**Solution :**

**Fill in the Blanks**

In questions 13 to 46, fill in the blanks to make the statements true.

**Question 13:** is a rational number

**Solution :**

The given rational number is a negative number, because its numerator is negative integer.

Hence, is a negative rational number.

**Question 14:**is a____rational number.

**Solution :**

The given rational number 1 is positive number, because its numerator and denominator are positive integer.

Hence, 1 is a

**positive**rational number.

**Question 15:**The standard form of is______ .

**Solution :**

**Question 16:**The standard form of is______ .

**Solution :**

**Question 17:**On a number line, is to the______of Zero(0).

**Solution :**

**All the negative numbers lie on the left side of zero on the number line**

*Note***Question 18:**On a number line, is to the______of Zero(0).

**Solution :**

On a number line, is to the

**right**of Zero(0).

**Note**All the positive numbers lie on the right side of zero on the number line.

**Question 19:** is _____ than .

**Solution :**

**Question 20:** is _____ than 0.

**Solution :**

**Question 21:** and represent_______ rational numbers.

**Solution :**

**Question 22:** and represent_______ rational numbers.

**Solution :**

**Question 23:**Additive inverse of is_____.

**Solution :**

Since, additive inverse is the negative of a number.

Hence, additive inverse of is .

**Note**Additive inverse is a number, which when added to a given number, we get result as zero.

**Question 24:** + = _____.

**Solution :**

**Question 25:** + = ______.

**Solution :**

**Question 26:** = _____.

**Solution :**

**Question 27:** = _____.

**Solution :**

**Question 28:**Given,

**Solution :**

**Question 29:** =

**Solution :**

**Question 30:** – = _____

**Solution :**

**In questions 31 to 35, fill in the boxes with the correct symbol ‘<‘,'<‘ or ‘=’.**

**Question 31:**

**Solution :**

**Question 32:**

**Solution :**

**Question 33:**

**Solution :**

**Question 34:**

**Solution :**

**Question 35:**

**Solution :**

**Question 36:**The reciprocal of_______ does not exist.

**Solution :**

The reciprocal of zero does not exist, as reciprocal of 0 is 1/0, which is not defined.

**Question 37:**The reciprocal of 1 is_______

**Solution :**

The reciprocal of 1=1/1

Hence, the reciprocal of 1 is 1.

**Question 38:** =________

**Solution :**

**Question 39:** =_________

**Solution :**

**Question 40:** =_________

**Solution :**

Hence, =0

Because, zero multiplies by any number result is zero.

**Question 41:**_____ x =1

**Solution :**

**Question 42:**The standard form of rational number – 1 is_______.

**Solution :**

∴ HCF of given rational number -1 is 1.

For standard form = -1 +1 = -1

Hence, the standard form of rational number -1 is -1.

**Question 43:** If m is a common divisor of a and b, then

**Solution :**

**Question 44:**If p and q are positive integers, then is a______ rational number and is a_____ rational number.

**Solution :**

if p and q are positive integers, then p/q is a

**positive**rational number, because both numerator and denominator are positive and is a

**negative**rational number, because denominator is in negative

**Question 45:**Two rational numbers are said to be equivalent or equal, if they have the same_______form.

**Solution :**

Two rational numbers are said to be equivalent or equal, if they have the same

**simplest**form.

**Question 46:**If p/q is a rational number, then q cannot be_____________

**Solution :**

By definition, if B is a rational number, then q cannot be

**zero**.

**True/False**

In questions 47 to 65, state whether the following statements are True or False.

**Question 47:**Every natural number is a rational number, but every rational number need not be a natural number.

**Solution :**

**True**

e.g. 1/2 is a rational number, but not a natural number.

**Question 48:**Zero is a rational number.

**Solution :**

**True**

e.g. Zero can be written as 0 = 0/1. We know that, a number of the form , where p, q are integers and q ≠ 0 is a rational number. So, zero is a rational number.

**Question 49:**Every integer is a rational number but every rational number need not be an integer.

**Solution :**

**True**

Integers…. – 3,-2,-1, 0,1,2, 3,…

Rational numbers:

……

Hence, every integer is rational number, but every rational number is not an integer.

**Question 50:**Every negative integer is not a negative rational number.

**Solution :**

**False**

Because all the integers are rational numbers, whether it is negative/positive but vice-versa is not true.

**Question 51:**If is a rational number and m is a non-zero integer, then

**Solution :**

**True**

e.g. Let m = 1,2, 3,…

*Note:**When both*numerator and denominator of a rational number are multiplied/divide by a same non-zero number, then we get the same rational number

**Question 52:**If is a rational number and m is a non-zero common divisor of p and q, then

**Solution :**

**Question 53:**In a rational number, denominator always has to be a non-zero integer.

**Solution :**

Basic definition of the rational number is that, it is in the form of , where q ≠ 0. It is because any number divided by zero is not defined.

**Question 54:**If is a rational number and m is a non-zero integer, then is a rational number not equivalent to .

**Solution :**

**Question 55:**Sum of two rational numbers is always a rational number.

**Solution :**

**True**

Sum of two rational numbers is always a rational number, it is true.

**Question 56:**All decimal numbers are also rational numbers.

**Solution**

**True**

All decimal numbers are also rational numbers, it is true.

**Question 57:**The quotient of two rationals is always a rational number.

**Solution :**

**False**

The quotient of two rationals is not always a rational number.

e.g. 1/0.

**Question 58:**Every fraction is a rational number.

**Solution :**

**True**

Every fraction is a rational number but vice-versa is not true.

**Question 59:**Two rationals with different numerators can never be equal.

**Solution :**

**False**

**Question 60:**8 can be written as a rational number with any integer as denominator.

**Solution :**

8 can be written as a rational number with any integer as denominator, it is false because 8 can be written as a rational number with 1 as denominator i.e.8/1.

**Question 61:** is equivalent to

**Solution :**

**True**

**Question 62:**The rational number lies to the right of zero on the number line.

**Solution :**

**False**

**Question 63:**The rational number and are on the opposite sides of zero on the number line.

**Solution :**

**Question 64:**Every rational number is a whole number.

**Solution :**

**False**

e.g. is a rational number, but it is not a whole number, because whole numbers are 0,1,2….

**Question 65:**Zero is the smallest rational number.

**Solution :**

**False**

Rational numbers can be negative and negative rational numbers are smaller than zero.

**Question 66:**Match the following:

**Solution :**

**Question 67:**Write each of the following rational numbers with positive denominators.

**Solution :**

**Question 68:**Express as a rational number with denominator:

(a)36 (b) — 80

**Solution :**

**Question 69:**Reduce each of the following rational numbers in its lowest form

(i)

(ii)

**Solution :**

**Question 70:**Express each of the following rational numbers in its standard form

**Solution :**

**Question 71:**Are the rational numbers and equivalent? Give reason.

**Solution :**

**Question 72:**Arrange the rational numbers in ascending order.

**Solution :**

**Question 73:**Represent the following rational numbers on a number line.

**Solution :**

**Question 74:**If = find the value of x.

**Solution :**

**Question 75:**Give three rational numbers equivalent to

(i)

(ii)

**Solution :**

**Question 76:**Write the next three rational numbers to complete the pattern:

**Solution :**

**Question 77:**List four rational numbers between and .

**Solution :**

**Question 78:**Find the sum of

**Solution :**

**Question 79:**Solve:

**Solution :**

**Question 80:**Find the product of

**Solution :**

**Question 81:**Simplify:

**Solution :**

**Question 82:**Simplify:

**Solution :**

**Question 83:**Which is greater in the following?

**Solution :**

**Question 84:**Write a rational number in which the numerator is less than ‘-7 x 11′ and the denominator is greater than ’12+ 4’.

**Solution :**

**Question 85:**If x = and y = , then evaluate x + y, x-y, xxy and x ÷ y.

**Solution :**

**Question 86:**Find the reciprocal of the following:

**Solution :**

**Question 87:**Complete the following table by finding the sums.

**Solution :**

**Question 88:**Write each of the following numbers in the form p/q, where p and q are integers.

(a) six-eighths (b) three and half

(c) opposite of 1 (d) one-fourth

(e) zero (f) opposite of three-fifths

**Solution :**

**Question 89:** =

**Solution :**

**Question 90:**Given that, and are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers, we say that

**Solution :**

**Question 91:**In each of the following cases, write the rational number whose numerator and denominator are respectively as under:

(a) 5-39 and 54-6 (b) (- 4) x 6 and 8 ÷ 2

(c) 35 ÷ (- 7) and 35 -18 (d) 25 +15 and 81÷40

**Solution :**

**Question 92:**Write the following as rational numbers in their standard forms.

**Solution :**

**Question 93:**Find a rational number exactly halfway between

**Solution :**

**Question 94:****Solution :**

**Question 95:**What should be added to to obtain the nearest natural number?

**Solution :**

**Question 96:**What should be subtracted from to obtain the nearest integer?

**Solution :**

**Question 97:**What should be multiplied with to obtain the nearest integer?

**Solution :**

**Question 98:**What should be divided by to obtain the greatest negative integer?

**Solution :**

**Question 99:**From a rope 68 m long, pieces of equal size are cut. If length of one piece is m, find the number of such pieces.

**Solution :**

**Question 100:**If 12 shirts of equal size can be prepared from 27 m cloth, what is length of cloth required for each shirt?

**Solution :**

**Question 101:**Insert 3 equivalent rational numbers between

**Solution :**

**Question 102:**Put the (✓), wherever applicable

**Solution :**

**Question 103:**‘o’ and ‘b’ are two different numbers taken from the numbers 1-50. What is the largest value that can have? What is the largest can have?

**Solution :**

**Question 104:**150 students are studying English, Maths or both. 62% of the students are studying English and 68% are studying Maths. How many students are studying both?

**Solution :**

**Question 105:**A body floats of its volume above the surface. What is the ratio of the body submerged volume to its exposed volume? Rewrite it as a rational number.

**Solution :**

In questions 106 to 109, find the odd one out of the following and give reason.

**Question 106:****Solution :**

**Question 107:****Solution :**

**Question 108:****Solution :**

**Question 109:**

**Solution :**From the above given rational numbers, we can see that is in its lowest form while others have common factor in numerator and denominator.

**Question 110:**What’s the Error? Chhaya simplified a rational number is this manner = What error did the student make?

**Solution :**

**All Chapter NCERT Exemplar Problems Solutions For Class 7 maths**

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